Well Texas and California both had brief periods OTL as independent republics, although both of them had the desire to be incorporated in to the USA pretty much from the get-go.
As society like the Draka, where you have a relatively small citizen class and a very large serf/slave class will inevitably begin to develop gender equality - it's not really about lesbian ninjas. In the USA, the ACW did a lot for gender equality as with so many men away women had to literally mind the store and take on previously more male roles. Of course WWI and WWII added on to this. Here with basically every physically fit male in the reserve system, and it is inevitable that with Draka expansion reserve units will have call ups for combat duty, the women at home are going to have to be involved in managing farms, businesses etc. Additionally they really need to be competent and comfortable with firearms to deal with any potential serf disturbances. With a relatively thin crust of citizens, the Domination cannot afford to be exclusionary of women in higher (university) education and I expect you'll see female lawyers, doctors, scientists, engineers sooner there than elsewhere. Of course the need for women to have children, and large citizen families would be encouraged, means there are limits on gender equality especially before more modern medicine and so forth however there is no reason this "talent pool" cannot be exploited.
Here you have cultural necessity pushing towards gender equality more strongly and sooner than OTL, at least in the Domination. Unlike Muslim countries, and many other cultural centers, such pushback as their might be towards gender equality will be much weaker. To use the example of Saudi Arabia, where women more or less need to be with a male relative most of the time out of the house, and until recently could not even drive, you have a situation where the talents of half of the population are grossly underutilized. Unlike the Saudis, and if they ever run out of oil money this will be a problem, the Draka at this point can't afford that sort of thinking, and once "equality" happens it won't be reversed.